# How do you solve #x^2+4x+7=0#?

##### 1 Answer

Try factoring first. It won't work, so either use the quadratic formula or complete the square, as you prefer.

#### Explanation:

The expression will not factor using integers.

Use your favorite of either the quadratic formula or completing the square.

**Completing the square**

Because the leading coefficient is

Which has no solution in the Real Numbers, but has 2 imaginary solutions in the Complex Numbers.

**Quadratic formula**

# = (-4+-sqrt(16-28))/2#

# = (-4+-sqrt(-12))/2#

Which has no solution in the Real Numbers, but has 2 imaginary solutions in the Complex Numbers.

# = (-4+- 2isqrt(3))/2#

# = -2 +- isqrt3#